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Mathematics 15 Online
OpenStudy (mathmath333):

A question

OpenStudy (mathmath333):

OpenStudy (mathmath333):

|dw:1455375697600:dw|

OpenStudy (anonymous):

what do you think

OpenStudy (anonymous):

i got 2:3

OpenStudy (mathmath333):

how u got 2:3

jhonyy9 (jhonyy9):

so milk and water has ratio 3/2 - this mean that there are 3 milk and 2 water 3/2 = 1,5 increased by 10% milk 1,5 ----- 100% x ------- 10% -------------- x = 1,5 *10/100 = 0,15 so this ratio 1,5 increased by 10% will be equal 1,65 but because the milk percent was increased by 10% so than 3 ----- 100% x ------ 10% -------------- x = 3*10/100 = 0,3 so this result that the ratio will be 3,3/2 what mean 3,3 milk and 2 water hope this will help you

OpenStudy (mathmath333):

is the answer 7/4

OpenStudy (mathmath333):

and is this 1,5 1 coma 5 or 1 dot 5

OpenStudy (mathmath333):

is it 33/20

jhonyy9 (jhonyy9):

@agent0smith so exactly what i have wrote above - very nice

OpenStudy (mathmath333):

u mean answer is 33/20

OpenStudy (agent0smith):

@jhonyy9 yours was unnecessarily long and hard to read. I assumed the asker knew how to find 10% of 3.

OpenStudy (mathmath333):

0.3

OpenStudy (michele_laino):

here is my reasoning: the initial volume \(V_i\) of solution, is given by this formula: \[\Large {V_i} = {v_m} + {v_w},\quad {v_m} = \frac{3}{2}{v_w}\] where \(v_m\) and \(v_w\) are the volumes of the milk and water respectively

OpenStudy (agent0smith):

Oh I see, the volume of the whole solution is increased by 10% by adding milk, it's not the volume of milk that is increased by 10%.

OpenStudy (agent0smith):

You can still do it with ratios. The ratio was 3 : 2, so total volume is 5. So 0.5 was added,10% of the total 5. It was all milk. So new ratio is 3.5 : 2

jhonyy9 (jhonyy9):

@nikolai11111

OpenStudy (anonymous):

hi

OpenStudy (anonymous):

i needhelp

jhonyy9 (jhonyy9):

tag me there

OpenStudy (anonymous):

where

jhonyy9 (jhonyy9):

where is your question

OpenStudy (anonymous):

ok

OpenStudy (anonymous):

\[3+\sqrt{x+19-}\sqrt{2} when x =6\]

jhonyy9 (jhonyy9):

@nikolai11111 please rewrite your exercise on the open question column - ok. ?

OpenStudy (anonymous):

idk how to do that

OpenStudy (michele_laino):

now, the final volume \(V_f\), of such solution, is: \[\Large {V_f} = {V_i} + 0.1{V_i} = 1.1{V_i}\] furthermore, we can write: \[\Large v{'_m} = kv{'_w}\] where \(k\) is the coefficient which has to be determined Developing the formula for \(V_f\), we get: \[\Large v{'_m} + v{'_w} = 1.1{V_i} = 1.1\left( {{v_m} + {v_w}} \right)\] where \(v'_m\) and \(v'_w\) are the volumes of milk and water after the dilution. Now, we have: \[\Large v{'_w} = {v_w},\quad v{'_m} = kv{'_w} = k{v_w}\] since the volume of water is unchanged Next, we make some substitutions: \[\Large k{v_w} + {v_w} = 1.1\left( {\frac{3}{2}{v_w} + {v_w}} \right)\] from which I get: \[\Large k = \frac{7}{4}\]

OpenStudy (anonymous):

jhon are u there

OpenStudy (mathmath333):

thnx

OpenStudy (michele_laino):

:)

OpenStudy (mathmath333):

:)

OpenStudy (agent0smith):

@mathmath333 and @michele_laino it is far easier to just use ratios :)

OpenStudy (michele_laino):

yes! that's right!

OpenStudy (anonymous):

michele can u help me

OpenStudy (agent0smith):

@mathmath333 if you missed it, this is how to do it using ratios: The milk:water ratio was 3 : 2, so the total volume is 5. 0.5 was added, 10% of the total volume. It was all milk. So the new ratio is 3.5 : 2 Then just simplify that by doubling both sides.

OpenStudy (mathmath333):

yes that is easy

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